We see that \(V_{i}\)  contains the `Vandermonde'-like rows and \(G_{i}\)  contains the `Gabidulin'-like rows. Also note that the powers of \(x_{i,j}\)  are increasing steadily from 0 to \(t+m-1\)  (which is equal to \(ag+h-1\) ); first along \(A_i\) , then \(V_i\)  and then the first row of \(G_i\)  (when expressed in \({\mathbb {F}}_q\)  basis). This is the most crucial part of the construction as we will shortly see. The MR LRC constructions from [1]}, [2]} also use a similar trick.
